Abstract:
This talk is devoted to the study of new families of orthonormal wavelets (e.g., Vieta-Lucas wavelets). We first compute their Fourier transform. Moreover, the use of connection coefficients allow us to deal with their differentiability. We therefore expand the mother wavelet in Taylor series to introduce the concept of local fractional derivative. Finally, we give an application in terms of function spaces and sampling techniques.
References:
[1] Biazar, J.; Ebraimi, H. Chebyshev wavelets approach for nonlinear systems of Volterra integral equations. Comput. Math. with Appl. 2012, 63(3), 608–616.
[2] Chalice, D. A characterization of the Cantor function, Am. Math. Mon. 1991, 98(3), 255–258.
[3] Daubechies I. Ten Lectures on Wavelets; SIAM: Philadelphia, PA, USA, 1992.
[4] Guariglia, E.; Guido, R.C. Chebyshev wavelet analysis. J. Funct. Spaces 2022, 2022(1), Art. No. 5542054.
[5] Horadam, A.F. Vieta Polynomials. Fibonacci Quart. 2002, 40(3), 223–232.
[6] Mallat, S.G. A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Anal. Mach. Intell. 1989, 11(7), 674–693.
[7] Tasci, D.; Yalcin, F. Vieta-Pell and Vieta-Pell-Lucas polynomials. Adv. Differ. Equ. 2013, 2013(1), Art. No. 224.
Biography:
Dr. Emanuel Guariglia received his B.Sc. and M.Sc. degrees in Telecommunications Engineering from the University of Naples Federico II, Naples, in 2010 and 2013. He received his Ph.D. degree in Mathematics from the University of Salerno, Fisciano, in 2017. During his PhD, he won the Best Student Award at the ICNPAA 2016 World Congress (La Rochelle, France, 4-8 July, 2016) for the scientific paper titled “A functional derivative for the Riemann zeta fractional derivative”.
After 3 years in Italy as adjunct professor of Calculus, he engaged in as a Postdoctoral Researcher at São Paulo State University (Brazil) in wavelet analysis under the supervision of Rodrigo Capobianco Guido (2020-2022). Apart from wavelet analysis, his research interests include fractal geometry, applied functional analysis, fractional calculus, analytic number theory and dynamical systems. To date, he has published over 21 papers contributing to his areas of research in peer-reviewed journals and has been an invited speaker at many international conferences. He was an invited speaker at several relevant international conferences in line with his areas of research from Europe to Southern America. He is currently an editorial board member of different peer-reviewed international scientific journals. Dr. Emanuel Guariglia is in the world’s Top 2% Scientists most-cited scientists by Stanford University.